We will describe natural infinite collections of random (Brownian) loops, some of their nice features, and how they are related to some basic ideas and concepts from physics. We will in particular focus on some underlying intriguing random geometric objects in d-dimensional space, and how their construction and behavior drastically differ when d=3, 4 and 5.
About Wendelin Werner:
Wendelin Werner (born 1968) is a German-born French mathematician working on random processes such as self-avoiding random walks, Brownian motion, Schramm-Loewner evolution, and related theories in probability theory and mathematical physics. He is professor at ETH Zurich.
In 2006, he received the Fields Medal for his contribution to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory. He was also honoured with the Rollo Davidson Prize in 1998, the Fermat Prize in 2001, the Grand Prix Jacques Herbrand of the French Academy of Sciences in 2003, the Loève Prize in 2005, the SIAM George Pólya Prize in 2006 and the Heinz Gumin Prize in 2016. He is a member of the French Academy of Sciences, the Academy of Sciences Leopoldina and the Berlin-Brandenburg Academy of Sciences.